The field of the disclosure relates generally to downhole measurement systems and, more particularly, to systems and methods for computing downhole pump position and load.
Most known rod pumping units (also known as surface pumping units) are used in wells to induce fluid flow, for example oil and water. The primary function of the pumping unit is to convert rotating motion from a prime mover (e.g., an engine or an electric motor) into reciprocating motion above the wellhead. This motion is in turn used to drive a reciprocating down-hole pump via connection through a sucker rod string. The sucker rod string, which can extend miles in length, transmits the reciprocating motion from the wellhead at the surface to subterranean valves in a fluid bearing zone of the well. The reciprocating motion of the valves induces the fluid to flow up the length of the sucker rod string to the wellhead.
The rod pumping units are exposed to a wide range of conditions. These vary by well application, the type and proportions of the pumping unit's linkage mechanism, and the conditions of the well. Furthermore, well conditions, such as downhole pressure, may change over time. These conditions may cause variability in the flow of the fluid. In addition, these conditions affect the sucker rod string. The sucker rod string transmits dynamic loads from the down-hole pump to the rod pumping unit. The sucker rod string behaves similarly to a spring over long distances. The sucker rod string elongates and retracts based on exposure to variable tensile stress. The response of the sucker rod string is damped somewhat due to its submergence in a viscous fluid (water and oil), but the motion profile of the rod pumping unit combined with the large variation of the load at the down-hole pump generally leaves little time for the oscillations to decay before the next perturbation is encountered.
The rod pumping unit imparts continually varying motion on the sucker rod string. The sucker rod string responds to the varying load conditions from the surface unit, down-hole pump, and surrounding environment by altering its own motion statically and dynamically. The sucker rod string stretches and retracts as it builds the force necessary to move the down-hole pump and fluid. The rod pumping unit, breaking away from the effects of friction and overcoming fluidic resistance and inertia, tends to generate counter-reactive interaction force to the sucker rod string exciting the dynamic modes of the sucker rod string, which causes an oscillatory response. Traveling stress waves from multiple sources interfere with each other along the sucker rod string (some constructively, others destructively) as they traverse its length and reflect load variations back to the rod pumping unit, where they can be measured. Translating measurements of these time-varying parameters, such as position and load, at the surface to downhole measurements is computationally intensive and typically involves use of partial differential equations, referred to as the wave equation. Consequently, computing time-varying downhole parameters is time consuming and complicates their use in controlling the rod pumping unit.